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Due to their non-trivial topology, skyrmions describe deflected trajectories, which hinders their straight propagation in nanotracks and can lead to their annihilation at the track edges. This deflection is caused by a gyrotropic force proportional to the topological charge and the angular momentum density of the host film. In this article we present clear evidence of the reversal of the topological deflection angle of skyrmions with the sign of angular momentum density. We measured the skyrmion trajectories across the angular momentum compensation temperature (TAC) in GdCo thin films, a rare earth/transition metal ferrimagnetic alloy. The sample composition was used to engineer the skyrmion stability below and above the TAC. A refined comparison of their dynamical properties evidenced a reversal of the skyrmions deflection angle with the total angular momentum density. This reversal is a clear demonstration of the possibility of tuning the skyrmion deflection angle in ferrimagnetic materials and paves the way for deflection-free skyrmion devices.

We show that subanalytic bi-Lipschitz homeomorphisms in general does not preserve the multiplicities of real analytic sets., Comment: We have omitted one possibility in Lemma 3.2. Now the Conjecture is still open

Even though the electromagnetic counterpart AT2017gfo to the binary neutron star merger GW170817 is powered by the radioactive decay of r-process nuclei, only few tentative identifications of light r-process elements have been made so far. One of the major limitations for the identification of heavy nuclei is incomplete or missing atomic data. While substantial progress has been made on lanthanide atomic data over the last few years, for actinides there has been less emphasis, with the first complete set of opacity data only recently published. We perform atomic structure calculations of neodymium $(Z=60)$ as well as the corresponding actinide uranium $(Z=92)$. Using two different codes (FAC and HFR) for the calculation of the atomic data, we investigate the accuracy of the calculated data (energy levels and electric dipole transitions) and their effect on kilonova opacities. For the FAC calculations, we optimise the local central potential and the number of included configurations and use a dedicated calibration technique to improve the agreement between theoretical and available experimental atomic energy levels (AELs). For ions with vast amounts of experimental data available, the presented opacities agree quite well with previous estimations. On the other hand, the optimisation and calibration method cannot be used for ions with only few available AELs. For these cases, where no experimental nor benchmarked calculations are available, a large spread in the opacities estimated from the atomic data obtained with the various atomic structure codes is observed.We find that the opacity of uranium is almost double the neodymium opacity., Comment: 20 pages, 13 figures. Accepted by MNRAS

In this paper we present some applications of A'Campo-L\^e's Theorem and we study some relations between Zariski's Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant when we consider right equivalence and this class contains many known classes of homeomorphisms that preserve tangent cones. In particular, we present some effective approaches to Zariski's Question A. We show a version of these results looking at infinity. Additionally, we present some results related with Nash modification and Lipschitz Geometry., Comment: 11 pages. To appear in Contemporary Mathematics

One fundamental obstacle to efficient ferromagnetic spintronics is magnetic precession, which intrinsically limits the dynamics of magnetic textures, We demonstrate that the domain wall precession fully vanishes with a record mobility when the net angular momentum is compensated (TAC) in DWs driven by spin-orbit torque in a ferrimagnetic GdFeCo/Pt track. We use transverse in-plane fields to reveal the internal structure of DWs and provide a robust and parameter-free measurement of TAC. Our results highlight the mechanism of faster and more efficient dynamics in materials with multiple spin lattices and reduced net angular momentum, promising for high-speed, low-power spintronics applications.

Ferrimagnetic TbFe or TbFeCo amorphous alloy thin films have been grown by co-evaporation in ultra-high vacuum. They exhibit an out-of-plane magnetic anisotropy up to their Curie temperature with a nucleation and propagation reversal mechanism suitable for current induced domain wall motion. Rutherford back scattering experiments confirmed a fine control of the Tb depth-integrated composition within the evaporation process. However, a large set of experimental techniques were used to evidence an interface related contribution in such thin films as compared to much thicker samples. In particular, scanning transmission electron microscopy experiments evidence a depth dependent composition and perturbed top and bottom interfaces with preferential oxidation and diffusion of terbium. Despite of that, amorphous and homogeneous alloy film remains in a bulk-like part. The composition of that bulk-like part of the magnetic layer, labeled as effective composition, is biased when compared with the depth-integrated composition. The magnetic properties of the film are mostly dictated by this effective composition, which we show changes with different top and bottom interfaces., Comment: 9 figures

It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture, constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity., Comment: 8 pages

Nitrogen-vacancy magnetic microscopy is employed in quenching mode as a non-invasive, high resolution tool to investigate the morphology of isolated skyrmions in ultrathin magnetic films. The skyrmion size and shape are found to be strongly affected by local pinning effects and magnetic field history. Micromagnetic simulations including static disorder, based on a physical model of grain-to-grain thickness variations, reproduce all experimental observations and reveal the key role of disorder and magnetic history in the stabilization of skyrmions in ultrathin magnetic films. This work opens the way to an in-depth understanding of skyrmion dynamics in real, disordered media., Comment: 9 pages, 8 figures, including supplementary informations

We address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are bi-Lipschitz homeomorphic at infinity must have the same degree. More specifically, we prove that the degree is a bi-Lipschitz invariant at infinity when the bi-Lipschitz homeomorphism has Lipschitz constants close to 1. In particular, we have that a family of complex algebraic sets bi-Lipschitz equisingular at infinity has constant degree. Moreover, we prove that if two polynomials are weakly rugose equivalent at infinity, then they have the same degree. In particular, we obtain that if two polynomials are rugose equivalent at infinity or bi-Lipschitz contact equivalent at infinity or bi-Lipschitz right-left equivalent at infinity, then they have the same degree., Comment: 13 pages. This is a minor revision of the last version with some changes in some definitions and proofs. To appear in the Proceedings of the American Mathematical Society

We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi-Lipschitz transformations (outer bi-Lipschitz homeomorphims of germs in the first case and outer bi-Lipschitz homeomorphims at infinity in the second case). We prove that invariance of multiplicity in the local case is equivalent to invariance of degree in the global case. We prove invariance for curves and surfaces. In the way we prove invariance of the tangent cone and relative multiplicities at infinity under outer bi-Lipschitz homeomorphims at infinity, and that the abstract topology of a homogeneous surface germ determines its multiplicity., Comment: 11 pages

We prove that any complex analytic set in $\mathbb{C}^n$ which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of $\mathbb{C}^n$ must be an affine linear subspace of $\mathbb{C}^n$ itself. No restrictions on the singular set, dimension nor codimension are required. In particular, a complex algebraic set in $\mathbb{C}^n$ which is Lipschitz regular at infinity is an affine linear subspace., Comment: Revision in the statement of Corollary 5.7 and it is added Example 5.8. 12 pages

We prove that tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. We also extend to real subanalytic sets the notion of reduced tangent cone and we show that subanalytic Lipschitz normally embedded sets have reduced tangent cones. In particular, we get that Lipschitz normally embedded complex analytic sets have reduced tangent cones., Comment: The paper was reorganized and also it was added an appendix by Anne Pichon and Walter D. Neumann. It has 13 pages and 6 figures

We prove that if two germs of irreducible complex analytic curves at $0\in\mathbb{C}^2$ have different sequence of characteristic exponents, then there exists $0<\alpha<1$ such that those germs are not $\alpha$-H\"older homeomorphic. For germs of complex analytic plane curves with several irreducible components we prove that if any two of them are $\alpha$-H\"older homeomorphic, for all $0<\alpha<1$, then there is a correspondence between their branches preserving sequence of characteristic exponents and intersection multiplicity of pair of branches. In particular, we recovery the sequence of characteristic exponents of the branches and intersection multiplicity of pair of branches are Lipschitz invariant of germs of complex analytic plane curves., Comment: 12 pages. Minor corrections in Example 4.16

This paper is devoted to study multiplicity and regularity as well as to present some classifications of complex analytic sets. We present an equivalence for complex analytical sets, namely blow-spherical equivalence and we receive several applications with this new approach. For example, we reduce to homogeneous complex algebraic sets a version of Zariski's multiplicity conjecture in the case of blow-spherical homeomorphism, we give some partial answers to the Zariski's multiplicity conjecture, we show that a blow-spherical regular complex analytic set is smooth and we give a complete classification of complex analytic curves., Comment: 24 pages. New references have been added, some typos have been corrected and some details have been added in the proof of Theorem 5.18

We carried out measurements of domain wall (DW) velocities driven by magnetic field pulses in symmetric Pt/Co/Pt and asymmetric Pt/Co/AlOx, Pt/Co/GdOx and Pt/Co/Gd trilayers with ultrathin Co layers and perpendicular magnetic anisotropy. In agreement with theoretical models, the maximum observed velocity is much larger in the asymmetric samples, where the interfacial Dzyaloshinskii-Moriya interaction (DMI) stabilises chiral N\'eel walls, than in the symmetric stack. In addition, in Pt/Co/Gd very large DW speeds (up to 600 m/s) are obtained, 2.5 times larger than in samples with oxidised Gd. Magnetic measurements reveal that this may be explained by the anti-parallel coupling between the magnetic moments of Gd and Co at the Gd/Co interface, leading to a decrease of the total magnetisation. In quantitative agreement with analytical models, in all samples the maximum observed DW speed scales as D=Ms, where D is the strength of the DMI and Ms the spontaneous magnetisation.

A model for a spin-torque nano-oscillator based on the self-sustained oscillation of a magnetic skyrmion is presented. The system involves a circular nanopillar geometry comprising an ultrathin film free magnetic layer with a strong Dzyaloshinkii-Moriya interaction and a polariser layer with a vortex-like spin configuration. It is shown that spin-transfer torques due to current flow perpendicular to the film plane leads to skyrmion gyration that arises from a competition between geometric confinement due to boundary edges and the vortex-like polarisation of the spin torques. A phenomenology for such oscillations is developed and quantitative analysis using micromagnetics simulations is presented. It is also shown that weak disorder due to random anisotropy variations does not influence the main characteristics of the steady-state gyration., Comment: 15 pages, 6 figures

In order to increase the thermal stability of a magnetic random access memory (MRAM) cell, materials with high spin-orbit interaction are often introduced in the storage layer. As a side effect, a strong Dzyaloshinskii-Moriya interaction (DMI) may arise in such systems. Here we investigate the impact of DMI on the magnetic cell performance, using micromagnetic simulations. We find that DMI strongly promotes non-uniform magnetization states and non-uniform switching modes of the magnetic layer. It appears to be detrimental for both the thermal stability of the cell and its switching current, leading to considerable deterioration of the cell performance even for a moderate DMI amplitude., Comment: 5 pages, 3 figures

We experimentally investigate the current-induced magnetization reversal in Pt/[Co/Ni]$_3$/Al multilayers combining the anomalous Hall effect and magneto-optical Kerr effect techniques in crossbar geometry. The magnetization reversal occurs through nucleation and propagation of a domain of opposite polarity for a current density of the order of 0.3 TA/m$^2$. In these experiments we demonstrate a full control of each stage: i)the {\O}rsted field controls the domain nucleation and ii) domain-wall propagation occurs by spin torque from the Pt spin Hall effect. This scenario requires an in-plane magnetic field to tune the domain wall center orientation along the current for efficient domain wall propagation. Indeed, as nucleated, domain walls are chiral and N\'eel like due to the interfacial Dzyaloshinskii-Moriya interaction., Comment: 5 pages, 3 figures

We give partial answers to a metric version of Zariski's multiplicity conjecture. In particular, we prove the multiplicity of complex analytic surface (not necessarily isolated) singularities in $\mathbb{C}^3$ is a bi-Lipschitz invariant., Comment: Accepted for publication by the Journal of Topology

We report on a new source of in-plane anisotropy in nanomagnets due to the presence of Dzyaloshinskii-Moriya interaction (DMI). This anisotropy depends on the shape of the magnet, and is orthogonal to the demagnetization shape anisotropy. This effect originates from the DMI energy reduction due to an out-of-plane tilt of the spins at edges oriented perpendicular to the magnetization. Our investigation combining experimental, numerical and analytical results demonstrate that this energy reduction can compensate the demagnetization shape anisotropy energy in magnets of elongated shape, provided that their volumes is small enough and thus that their magnetization is quasi-uniform., Comment: 5 pages, 4 figures

Facing the ever-growing demand for data storage will most probably require a new paradigm. Magnetic skyrmions are anticipated to solve this issue as they are arguably the smallest spin textures in magnetic thin films in nature. We designed cobalt-based multilayered thin films where the cobalt layer is sandwiched between two heavy metals providing additive interfacial Dzyaloshinskii-Moriya interactions, which reach about 2 mJ/m2 in the case of the Ir/Co/Pt multilayers. Using a magnetization-sensitive scanning x-ray transmission microscopy technique, we imaged magnetic bubble-like domains in these multilayers. The study of their behavir in magnetic field allows us to conclude that they are actually magnetic skyrmions stabilized by the Dzyaloshinsskii-Moriya interaction. This discoevry of stable skyrmions at room temperature in a technologically relevant material opens the way for device applications in a near future.

We prove that if there exists a bi-Lipschitz homeomorphism (not necessarily subanalytic) between two subanalytic sets, then their tangent cones are bi-Lipschitz homeomorphic. As a consequence of this result, we show that any Lipschitz regular complex analytic set, i.e any complex analytic set which is locally bi-lipschitz homeomorphic to an Euclidean ball must be smooth. Finally, we give an alternative proof of S. Koike and L. Paunescu's result about the bi-Lipschitz invariance of directional dimensions of subanalytic sets., Comment: 7 pages

The magnetostatic interaction between magnetic domain walls (DWs) in adjacent nanotracks has been shown to produce strong inter-DW coupling and mutual pinning. In this paper, we have used electrical measurements of adjacent spin-valve nanotracks to follow the positions of interacting DWs. We show that the magnetostatic interaction between DWs causes not only mutual pinning, as observed till now, but that a travelling DW can also induce the depinning of DWs in near-by tracks. These effects may have great implications for some proposed high density magnetic devices (e.g. racetrack memory, DW logic circuits, or DW-based MRAM)., Comment: The following article has been accepted by the Journal of Applied Physics

The increasing number of objects orbiting the Earth justifies the great attention and interest in the observation, spacecraft protection and collision avoidance. These studies involve different disturbances and resonances in the orbital motions of these objects distributed by the distinct altitudes. In this work, the TLE (Two-Line Elements) of the NORAD are studied observing the resonant period of the objects orbiting the Earth and the main resonance in the LEO region. The time behavior of the semi-major axis, eccentricity and inclination of some space debris are studied. Possible irregular motions are observed by the frequency analysis and by the presence of different resonant angles describing the orbital dynamics of these objects., Comment: 22 pages, 37 figures, submitted to Acta Astronautica

Being E a vector space with inner product and S the sphere of E, will be given a demonstration that every application of the sphere S itself it such that preserve inner product is the restriction of a linear isometry in E., Comment: 3 pages

This article was withdrawn by the author to be incorporated into the paper "Extens\~ao de aplica\c{c}\~oes na esfera de um espa\c{c}o vetorial com produto interno" (arXiv:1109.2866)., Comment: This article was withdrawn by the author to be incorporated into the paper "Extens\~ao de aplica\c{c}\~oes na esfera de um espa\c{c}o vetorial com produto interno", arXiv:1109.2866

The temperature dependence of the electrical resistivity in insulator systems with a Coulomb gap in the density of states is expressed by a very simple function which coincides with the Efros-Shklovskii T^(-1/2)result, at temperatures lower than some value Tlim. Above this limit it consists of the product of the Mott T^(-1/4) exponential with another one like a simply thermally activation process. It fits well several experimental results reported as having a crossover between the Efros-Shklovskii and Mott regimes, and allows the determination of the gap parameters even in experiments that do not reach the T^(-1/2) regime. Also it accounts for some experimental results reported to follow a T^(-n) behavior with 0.5

Electron captures on nuclei play an important role in the dynamics of the collapsing core of a massive star that leads to a supernova explosion. Recent calculations of these capture rates were based on microscopic models which account for relevant degrees of freedom. Due to computational restrictions such calculations were limited to a modest number of nuclei, mainly in the mass range A=45-110. Recent supernova simulations show that this pool of nuclei, however, omits the very neutron-rich and heavy nuclei which dominate the nuclear composition during the last phase of the collapse before neutrino trapping. Assuming that the composition is given by Nuclear Statistical Equilibrium we present here electron capture rates for collapse conditions derived from individual rates for roughly 2700 individual nuclei. For those nuclei which dominate in the early stage of the collapse, the individual rates are derived within the framework of microscopic models, while for the nuclei which dominate at high densities we have derived the rates based on the Random Phase Approximation with a global parametrization of the single particle occupation numbers. In addition, we have improved previous rate evaluations by properly including screening corrections to the reaction rates into account., Comment: 32 pages, 13 figures, 1 table; elsart; to appear in Nuclear Physics A

The magnetostatic interaction between two oppositely charged transverse domain walls (DWs)in adjacent Permalloy nanowires is experimentally demonstrated. The dependence of the pinning strength on wire separation is investigated for distances between 13 and 125 nm, and depinning fields up to 93 Oe are measured. The results can be described fully by considering the interaction between the full complex distribution of magnetic charge within rigid, isolated DWs. This suggests the DW internal structure is not appreciably disturbed by the pinning potential, and that they remain rigid although the pinning strength is significant. This work demonstrates the possibility of non-contact DW trapping without DW perturbation and full continuous flexibility of the pinning potential type and strength. The consequence of the interaction on DW based data storage schemes is evaluated., Comment: 4 pages, 4 figures, 1 page supplimentary material (supporting.ps)

Based on the shell model for Gamow-Teller and the Random Phase Approximation for forbidden transitions, we have calculated reaction rates for inelastic neutrino-nucleus scattering (INNS) under supernova (SN) conditions, assuming a matter composition given by Nuclear Statistical Equilibrium. The rates have been incorporated into state-of-the-art stellar core-collapse simulations with detailed energy-dependent neutrino transport. While no significant effect on the SN dynamics is observed, INNS increases the neutrino opacities noticeably and strongly reduces the high-energy tail of the neutrino spectrum emitted in the neutrino burst at shock breakout. Relatedly the expected event rates for the observation of such neutrinos by earthbound detectors are reduced by up to about 60%., Comment: 4 pages, 2 figures, 1 table

We study neutral current neutrino-nucleus reaction cross-sections for Mn, Fe, Co and Ni isotopes. An earlier study for a few selected nuclei has shown that in the supernova environment the cross sections are increased for low energy neutrinos due to finite-temperature effects. Our work supports this finding for a much larger set of nuclei. Furthermore we extend previous work to higher neutrino energies considering allowed and forbidden multipole contributions to the cross sections. The allowed contributions are derived from large-scale shell model calculations of the Gamow-Teller strength, while the other multipole contributions are calculated within the Random Phase Approximation. We present the cross sections as functions of initial and final neutrino energies and for a range of supernova-relevant temperatures. These cross sections will allow improved estimates of inelastic neutrino reactions on nuclei in supernova simulations., Comment: 26 pages, 15 figures, submitted to Nuclear Physics A

The most important weak nuclear interaction to the dynamics of stellar core collapse is electron capture, primarily on nuclei with masses larger than 60. In prior simulations of core collapse, electron capture on these nuclei has been treated in a highly parameterized fashion, if not ignored. With realistic treatment of electron capture on heavy nuclei come significant changes in the hydrodynamics of core collapse and bounce. We discuss these as well as the ramifications for the post-bounce evolution in core collapse supernovae., Comment: Accepted by PRL, 5 pages, 2 figures

Supernova simulations to date have assumed that during core collapse electron captures occur dominantly on free protons, while captures on heavy nuclei are Pauli-blocked and are ignored. We have calculated rates for electron capture on nuclei with mass numbers A=65-112 for the temperatures and densities appropriate for core collapse. We find that these rates are large enough so that, in contrast to previous assumptions, electron capture on nuclei dominates over capture on free protons. This leads to significant changes in core collapse simulations., Comment: 5 pages, 4 figures, REVTeX 4

Electron capture rates on neutron-rich nuclei (A>65) were calculated within the Random Phase Approximation with partial number formalism, including allowed and forbidden transitions. The partial occupation numbers were provided as a function of temperature by Shell-Model Monte Carlo calculations, including an pairing+quadrupole interaction. Capture rates on relevent nuclei were calculated for density and temperature conditions during the core collapse of a massive star. It was found that electron captures on nuclei can compete with electron captures on free protons. Furthermore, they produce neutrinos with average energies lower than neutrinos emitted from captures on free protons, with possible consequences on the cooling of the core., Comment: 3 pages, 4 figures, submitted to the proceedings of Nuclei in the Cosmos XVII

We perform large-scale shell model Monte Carlo (SMMC) calculations for many nuclei in the mass range A=56-65 in the complete pfg_{9/2}d_{5/2} model space using an effective quadrupole-quadrupole+pairing residual interaction. Our calculations are performed at finite temperatures between T=0.33-2 MeV. Our main focus is the temperature dependence of the symmetry energy which we determine from the energy differences between various isobaric pairs with the same pairing structure and at different temperatures. Our SMMC studies are consistent with an increase of the symmetry energy with temperature. We also investigate possible consequences for core-collapse supernovae events.

We study the neutral-current neutrino scattering for four nuclei in the iron region. We evaluate the cross sections for the relevant temperatures during the supernova core collapse and derive Gamow-Teller distributions from large-scale shell-model calculations. We show that the thermal population of the excited states significantly enhances the cross sections at low neutrino energies. Calculations of the outgoing neutrino spectra indicate the prospect of neutrino upscattering at finite temperatures. Both results are particularly notable in even-even nuclei., Comment: 14 pages, 4 figures, accepted in Phys. Lett. B)

We study charged-current neutrino cross sections on neutronrich nuclei in the mass $A\sim60$ region. Special attention is paid to environmental effects, i.e. finite temperature and density, on the cross sections. As these effects are largest for small neutrino energies, it is sufficient to study only the Gamow-Teller (GT) contributions to the cross sections. The relevant GT strength distributions are derived from large-scale shell model calculations. We find that the low-energy cross sections are enhanced at finite temperatures. However, for $(\nu_e,e^-)$ reactions Pauli blocking of the electrons in the final state makes the cross sections for low-energy neutrinos much smaller than for the competing inelastic scattering on electrons at moderate and large densities. Absorption cross sections for low-energy antineutrinos are strongly enhanced at finite temperatures., Comment: 11 pages, 4 figures